Math Challenges - 2023 每月問題 (1月份問題)
小學組 (Primary Section)
如果從2至11這十個數中取去其中一對數(即兩個數)，使餘下八個數之和是一個質數，這樣的數有幾多對？
If a pair of numbers (two numbers) are taken away from the ten numbers 2,3,…,11, the sum of the remaining eight numbers is a prime number. How many such pairs of numbers are there?
初中組 (Junior Secondary Section)
N 是一個小於1000的正整數，它有十個因數，其中兩個是4和62，設這十個因數之和是 S 。求 
。
N is a positive integer less than 1000 and has exactly ten factors. Two of these factors are 4 and 62. Let the sum of these ten factors be S . Find .
高中組 (Senior Secondary Section)
二人輪流擲三顆骰子，誰先擲出總點數是平方數者勝。這個遊戲對先擲者還是後擲者有利？
Two persons roll three dice in turn. Whoever gets a sum that is a square number will be the winner. Who will this game favour, the person rolling first or second?
参加辦法
参加同學請把以下資料載於不多於兩頁A4紙的 PDF格式(不接受其他格式)的附件，於本月28日下午6時前電郵至monthlyproblems@eduhk.hk。
載於附件的資料包括：
- 完整題解和答案
- 以中、英文書寫的參加者姓名、年級、就讀學校名稱 和學校地址
- 聲明：「這題解是本人研習的成果。」
高中組不接受手寫題解，只接受電腦打印題解。
Participation Method
Put the following information in a PDF (other formats not accepted) file of not more than two A4 pages. Send the file as an email attachment to monthlyproblems@eduhk.hk by 6 pm on 28 Jan.
Information required:
- Solution to the problem
- Student name, year, school name, and school address (in both Chinese and English)
- Declaration: “This solution is my own work.”
Solutions to the senior secondary problem should be typewritten. Handwritten solutions to the senior secondary problem will not be accepted.
